{"id":"W2038240728","doi":"10.1016/j.jalgebra.2014.08.011","title":"Strong global dimension of commutative rings and schemes","year":2014,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"The Scarborough Hospital; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Global dimension; Mathematics; Noetherian; Indecomposable module; Dimension (graph theory); Local ring; Pure mathematics; Infimum and supremum; Commutative property; Noetherian ring; Krull dimension; Characterization (materials science); Dimension theory (algebra); Commutative ring; Ring (chemistry); Discrete mathematics; Algebra over a field","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001620342,0.0006670837,0.0008664085,0.002492927,0.002408315,0.00535373,0.0008454658,0.0006754948,0.006611502],"category_scores_gemma":[0.002765938,0.000615576,0.0005871822,0.001880731,0.006984574,0.0110493,0.003702629,0.002233221,0.0003152472],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001420078,"about_ca_system_score_gemma":0.0006442862,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007086316,"about_ca_topic_score_gemma":0.0009163691,"domain_scores_codex":[0.9991236,0.0002446066,0.00005135195,0.0001891207,0.0002197,0.0001715675],"domain_scores_gemma":[0.9970703,0.001295653,0.0004506753,0.0002660893,0.0003038499,0.0006134379],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000023788,0.000009205564,0.0005059289,0.00001355252,0.000006595391,0.00001874916,0.0002185148,0.000191614,0.0002022281,0.9974729,0.0001873888,0.001149453],"study_design_scores_gemma":[0.00001420388,0.00001368104,0.0008368322,0.000007903262,0.00001124974,0.00006017743,0.0001818231,0.000761863,0.0002090445,0.996298,0.001597468,0.000007647936],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8375069,0.003307481,0.05827815,0.0039669,0.0002411436,0.00003106223,0.000473357,0.0001213185,0.09607363],"genre_scores_gemma":[0.9907198,0.0005640863,0.002986352,0.0000972989,0.0002178998,0.00002059876,0.0001178688,0.00001448216,0.005261602],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006611502,"threshold_uncertainty_score":0.02211767,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01870280375215521,"score_gpt":0.296747061186072,"score_spread":0.2780442574339168,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}